Measurement of micro-harmonic vibration from optical feedback interferometry using wavelet trend analysis.

Self-mixed optical feedback interferometry based laser sensors show promising results in the measurement of the vibration frequency. To date several measurement methods have been developed to extract the vibration information from the self-mixed (SM) signal; however, the complexity and accuracy of the methods still need improvement. The presented work tries to fulfill the gap by realizing a novel method using maximal overlap discrete wavelet transformation (MODWT) and multi-resolution analysis (MRA). The proposed method can reconstruct the micro-harmonic (< ) vibration up to 1 kHz even under weak feedback conditions. The mean squared error and the maximum relative error of the proposed method for this range remained below 1.89 & 8.79%, respectively. Although, above 1 kHz, the proposed method turns out to be futile to reconstruct the vibration signal but still capable to measure vibration frequency up to 10 kHz with an accuracy of 0.0001. The method also found suitable to measure non-sinusoidal vibration frequency with reasonable accuracy even for the moderate feedback conditions. The authors envision that the proposed method will provide a compact, non-contact, and low-cost alternative for the vibration frequency measurement hence useful in early fault detection schemes and lung abnormality diagnosis.